Question

Create a system of equations

With the wind, an airplane travels 1120 miles in 7 hours. Against the wind, it takes 8 hours. Find the rate of the plane in still air, and the velocity of the wind. Remember: distance equals rate times time.

Answer 1

Let x and y be speeds of the airplane and wind respectively. Then,

With the wind: x+y = 1120/7 = 160 mph -------- (1)
Against the wind: x-y = 1120/8 = 140 mph --------- (2)

Solving equations (1) and (2)

Add equation (2) and equation (1)
x+y = 160
x-y = 140
------------
2x = 300 => x = 300/2 = 150 mph (speed of airplane in still air)
If the air was still, the airplane would take,

Time to 1120 miles in still air = Distance/speed = 1120/150 = 7.467 hours or 7 hours and 28 minutes.